The present invention relates generally to coherent PSK (phase shift keying) demodulators for M-ary PSK modulated convolutional codes, and more specifically, the present invention relates to a technique for recovering a carrier from a received PSK modulated convolutional code by precisely establishing synchronization with the received signal.
According to coherent detection which is used to demodulate a received M-ary PSK modulated convolutional code, the received signal is mixed with a local carrier to produce I- and Q-channel signals for coupling to a convolutional decoder and phase comparison is made between the demodulated signal and the local carrier to establish carrier synchronization. As described in Japanese Provisional Patent Publication (Tokkaisho) 59-12654, synchronization is established between the frequency of the recovered carrier and the symbol rate of received convolutional codes by detecting the error rate of the demodulated I- and Q-channel signals and reducing the error rate below a specified value through a feedback circuit. In this publication, a convolutional encoder is coupled to a convolution decoder. The output of the convolutional encoder and one input of the convolutional decoder are supplied to a correlator to determine their correlation. Since the output of the convolutional encoder is a replica of the original codeword, the correlator produces a signal which increases in amplitude with the error rate of the signal at the input of the convolutional decoder. A maximum detector is connected to the correlator to control the phase relation of the input signals of the convolutional decoder when the error rate exceeds a specified value.
However, the prior art technique tends to establish carrier synchronization even when the carrier frequency is not precisely coherent with the symbol rate of the received signal. Under this condition, the demodulator is said to be in a "quasi-coherent" state.
As an example of this quasi-coherent state, consider a BPSK system in which a 7-stage shift register S and exclusive OR gates A1 and A2 are used as a convolutional encoder as shown in FIG. 1. The bits stored in the first, second, third, fourth and seventh stages of the shift register S are supplied to exclusive OR gate A1 to produce a code word "171", and the bits stored in the first, third, fourth and sixth stages are supplied to exclusive OR gate A2 to produce a code word "133."
Let the input data stream at the input of a convolutional encoder be denoted by D.sub.n (D.sub.n =.+-.1) and let the output data stream from the convolutional encoder be denoted by C.sub.n.sup.171 and C.sub.n.sup.133, then the following relations hold:
C.sub.n.sup.171 =D.sub.n .times.D.sub.n-1 .times.D.sub.n-2 .times.D.sub.n-3 .times.D.sub.n-6 PA1 C.sub.n.sup.133 =D.sub.n .times.D.sub.n-2 .times.D.sub.n-3 .times.D.sub.n-5 .times.D.sub.n-6
where, all binary data are represented by +1 and -1.
If carrier synchronization is precisely established, the demodulated data streams become equal to C.sub.n.sup.171 and C.sub.n.sup.133 and by decoding such data streams by an error correction circuit, or convolutional decoder, the original data D.sub.n can be recovered. However, if carrier synchronization is not precise, the demodulated data streams will become C.sub.n.sup.171' and C.sub.n.sup.133' and the following relations will hold between error corrected data D'.sub.n and the original data stream D.sub.n : ##EQU1## Therefore, a decoding process properly proceeds and a decision is made that synchronization has been established.
It is appropriate to discuss to some length BPSK modulation and demodulation processes for codewords C.sub.n.sup.171' and C.sub.n.sup.133'.
Bit-parallel codewords C.sub.n.sup.171 and C.sub.n.sup.133 are converted to bit-serial data and supplied to a BPSK modulator producing the following data B.sub.m : ##EQU2## At the receive end, the demodulator produces bit-serial demodulated codewords B'.sub.m which are converted to bit-parallel codewords. If the codewords B'.sub.m have the following relations with the transmit data B'.sub.m ##EQU3## data streams C.sub.n.sup.171' and C.sub.n.sup.133' will result from a demodulation process.
The demodulated data stream B".sub.m will be given as follows if the frequency of the recovered carrier deviates as much as f.sub.s /4, where f.sub.s is the symbol rate of the transmitted signal: ##EQU4## The value B".sub.m is equal to B'.sub.m if binary levels are used for discrimination between a valid coherent state and a quasi-coherent state. Even if the frequency of the recovered carrier deviates by as small as 1/8 of the symbol rate, a quasi-coherent state can occur.